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Appendix IL                              849

.v be increased till it equals kL   Then BM1 = zero, or

from which, solving the quadratic,

x or $/ = "2i il.

Let a fixed beam A B be loaded in aay general or unsymme-
iriral manner as in Fig. Si 2, The curve of B,n for free load is
fcnmd at abc. The reactionary moment curve defg is next to
ins obtained. The two areas rz/'rant! defg must now not only

tt* i.'(}ual, but their rentroids nuist lie on a common vertical.
If then x shew the value of the free area ct^as also the position
wf its rcntroid, v and "/, tiuwt be placed at -|/ and of such value
* to             x in the manner of parallel forces, -where y 4- z  x.

'fhcn area /// -  and        dgf^t^ from whieh the moments ^^

!/ be ciedwred.     Lastly the resulting moment curve Bf
w t)taiiii!(I by sujperposition.

VIIL, Fig, 401, p. 443, k *hevrn in ciowbl^ at the top

of Fig, 81$ next

Bending Moments for Continuoms Girdera
The                        may be farther              to these